If you should learn a partner dance. Latin and tango are by far the most fun types of partner dancing IMHO. Learning how really boosts your confidence in asking chicks to dance/out on dates as well. Otherwise, swing is good, but it'll just get old after awhile if you don't graduate into lindy-hop. The thing about latin and tango is that they're such intimate dances. you have to be so close to the partner, and that just releases a very attractive, sensual atmoshpere, making the dance that much more fun.
There aren't many dojos around where I am, but if I could start up on Martial arts again, I'd try to learn from something more authentic than your run of the mill "John Doe's Karate academy". Those all just become tournament oriented and lose their philosophical qualities. If I were you, and I would stick to a discipline that teaches both hand-hand and weapon combat. Kung-Fu, Kenjutsu, or something of the like. Just search the net for more info, it's pretty easy to find.
The reason I suggest these is that they're graceful skills, requiring you to learn a great sense of coordination, as well as being great forms exercise and social activity.